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# Measuring temperature

## Thermometric properties

A thermometric property is a physical property that varies continuously with temperature.

Thermometric properties can be used to measure the temperature. Thermometric properties commonly used for thermometers include:

• Volume: Most objects expand when they are heated.

The volume of mercury or alcohol expands when the temperature increases. Both are often used in thermometers.

• Electrical resistance:

The resistance of a copper wire increases with temperature. Resistance thermometers use the resistance of copper or other metals to measure temperature.

The mass of an object does not change when an object is heated. Mass is not a thermometric property.

A thermometric property should be easily measurable.

People shiver when they get cold but this is not a good thermometric property. Shivering does not change continuously above a certain temperature (when it is warm) and shivering is difficult to measure.

The volume of a liquid inside a thermometer increases with temperature.

## Temperature scales

A temperature scale is a way of assigning a numerical value to a particular temperature.

This is similar to the length scale on a ruler (e.g. in inches or centimetres) in the measurement of length.

A temperature scale needs to be calibrated (marked so that it can be used in different situations) using at least two fixed points.

A fixed point is a standard known temperature like the boiling point of pure water.

Temperature scales can have different zero values and unit (interval) values.

The Celsius and Fahrenheit scales have different zero values $(0^{\circ}\text{C}=32^{\circ}\text{F})$ and different interval values. An interval of $1^{\circ}\text{F}$ is equal to an interval of $5/9^{\circ}\text{C}.$

Two thermometers calibrated according to the Celsius scale and the Fahrenheit scale.

The Celsius or centigrade temperature scale is the most common temperature scale in everyday use today, although in the US the Fahrenheit scale is more common.

The expected air temperature in the weather forecast is normally given in degrees Celsius or $^{\circ}\text{C}.$

The centigrade scale was originally defined using two fixed points:

• Steam point - The boiling point of pure water at one atmospheric pressure ($100^{\circ}\text{C}$)
• Ice point - The melting point of pure ice at one atmospheric pressure ($0^{\circ}\text{C}$)

These two reference points can be used to define any temperature.

The air temperature during one afternoon in July is $30 ^{\circ}\text{C}.$

Nowadays, two different fixed points are used to fix the centigrade scale more precisely.

The boiling point of water was used to define the Celsius temperature scale.

## Empirical temperature scales

An empirical temperature scale uses a specific thermometric property (a property that varies with temperature, such as volume, electric resistance) of a certain material (e.g. mercury).

The points of reference and the number of divisions within an empirical scale are essentially arbitrary.

An empirical scale can be obtained by measuring the length of a mercury column at the boiling point and at the freezing point of water (the reference points). The range between these two reference points is then divided into smaller units. This was the basis of the original Celsius scale.

The range of empirical scales is limited by the property of the material used to calibrate them.

Ethanol boils at $78^{\circ}\text{C}$. An empirical scale based on the volume expansion of liquid ethanol thus cannot be used to measure temperatures above $78^{\circ}\text{C}$ accurately.

It can be difficult to convert between different empirical scales because the variance of the thermometric property of the material used in calibrating a particular scale differs from that of other materials.

Ethanol and mercury have different rates of expansion. Calibrating a scale according to the properties of ethanol and using the same scale on a mercury thermometer would give inaccurate temperature readings.

## Absolute (thermodynamic) temperature scales

An absolute (or thermodynamic) temperature scale is a scale based on the phenomena underlying temperature, the movement of particles.

More specifically, absolute temperature scales have a common reference point (known as absolute zero). Absolute zero is the temperature at which the particles of a substance possess the lowest possible internal energy (i.e. there is no particle motion).

There can be no temperature that is lower than absolute zero. This point is derived through the laws of thermodynamics.

All other temperatures are extrapolated linearly upwards from absolute zero.

Absolute scales may differ in unit values (the size of steps between units).

The Kelvin and the Rankine scales are the only absolute scales in use today.

The Celsius and Fahrenheit temperature scales are empirical scales that were linearly extrapolated to cover the whole range of possible temperatures described by an absolute scale.

## Kelvin scale

The Kelvin scale is the most widely used absolute temperature scale in the scientific world.

It is defined and calibrated according to two points: absolute zero and the triple point of water.

• Absolute zero is the temperature at which the particles of a substance possess the lowest possible internal energy.
• The triple point of water is the point at which the three phases of water (i.e. solid, liquid and gas) exist in equilibrium.

The SI unit of the thermodynamic temperature scale is the kelvin ($\text{K}$).

The thermodynamic temperature and the Celsius temperature are related by:$$T (\text{K})=T(^{\circ}\text{C})+273.15$$$T (\text{K})$ is the temperature in kelvins and $T^{\circ}\text{C}$ is the temperature in degrees Celsius.

A temperature difference of one kelvin is equivalent in magnitude to a difference of one degree Celsius (i.e. $\vert1\text{ K}\vert=\vert1^{\circ}\text{C}\vert$).

## Calibrating liquid thermometers

The calibration of a thermometer involves marking the thermometer so that the temperature can be read accurately. The scale is based on the thermometric property used by the thermometer.

In a certain mercury thermometer, the mercury column is 3 cm long when the temperature is $0^{\circ}\text{C}$. If the thermometer was accurately calibrated, there should be a $0^{\circ}\text{C}$ marking at the 3 cm point.

To calibrate a thermometer using the Celsius scale without using another thermometer:

• Place the thermometer next to melting ice and record the length of the liquid column, $\Tblue{x_{1}}$.
• Place the thermometer in boiling water and record the length of the liquid column, $\Tred{x_{2}}$.

Only record the length of the liquid column once it has reached a steady level.

The temperature of an unknown source T (in $^{\circ}\text{C}$) can then be calculated: $$\Tgreen{\text{temperature}} = \frac{\Tgreen{x_{3}} - \Tblue{x_{1}}} {\Tred{x_{2}}-\Tblue{x_{1}} } \times 100$$

A thermometer is calibrated to the Celsius scale.

## How thermocouple thermometers work

A thermocouple thermometer determines the temperature by measuring a voltage generated as a result of the temperature difference between two wires (the thermoelectric effect).

In the setup in the image, three wires are used to connect a voltmeter to an object of known temperature (the cold junction) and an object of unknown temperature (second junction).

The temperature difference between the cold junction and the second junction generates a voltage between them. The bigger the temperature difference, the bigger the voltage.

If all the wires were made of the same metal, the voltage generated would be zero.

If the metal connecting the cold junction and the object of unknown temperature is different from the one connecting either of these objects to the voltmeter, a voltage is measured. The thermocouple is calibrated so that the temperature can be determined from the voltmeter reading.

A thermocouple thermometer.

## Benefits and drawbacks of thermocouple thermometers

Thermocouple thermometers measure temperatures by measuring the voltage induced as a result of temperature differences.

The advantages of thermocouple thermometers are that they:

• can be used to measure high temperatures because metals have high melting points,
• respond very quickly to temperature changes because metals have high conductivities and
• are sensitive to very small changes in temperature.

The main disadvantage of a thermocouple thermometer is that it is less accurate than a mercury thermometer.

A thermocouple thermometer